Question: Simplify the following expression: $ q = \dfrac{-7}{10} - \dfrac{7y + 6}{y + 8} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{y + 8}{y + 8}$ $ \dfrac{-7}{10} \times \dfrac{y + 8}{y + 8} = \dfrac{-7y - 56}{10y + 80} $ Multiply the second expression by $\dfrac{10}{10}$ $ \dfrac{7y + 6}{y + 8} \times \dfrac{10}{10} = \dfrac{70y + 60}{10y + 80} $ Therefore $ q = \dfrac{-7y - 56}{10y + 80} - \dfrac{70y + 60}{10y + 80} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{-7y - 56 - (70y + 60) }{10y + 80} $ Distribute the negative sign: $q = \dfrac{-7y - 56 - 70y - 60}{10y + 80}$ $q = \dfrac{-77y - 116}{10y + 80}$